Permutations and Combinations Practice Test

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1 Name: Class: Date: Permutations and Combinations Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Suppose that license plates in the fictional province of Mathistan consist of three unique letters followed by three unique numbers. The letters I and O cannot be used and the digits 1 and 0 cannot be used. Given these restrictions, how many potential license plates could be issued? a c b d How many permutations using all the letters of the word CELLULOSE are possible? a c. 720 b d In how many ways can a grand prize, a runner up prize and three identical consolation prizes be awarded to a group of 15 people. Assume that each person can win at MOST one prize. a c b d Use the following information to answer the next question Suppose that 6 members of the 12 students of the EPC basketball team are chosen to go to a special training camp in Calgary. Out of Brooke, Jackie, Brianna, and Alex, only two of them are guarranteed spots in the camp The remaining four spots will go to other eight players on the team. 4. How many potential ways can players be chosen to go to this camp? a. 840 c. 420 b. 140 d Suppose that five standard six-sided dice are rolled once. What is the number of possible results in which either all even numbers or all odd numbers are rolled? a. 486 c b d In how many ways can five parcels be delivered to three mailboxes if any number of parcels can go to any particular mailbox or combination of mailboxes. a. 3 5 c. 5 3 b. P 5 3 d. C How many potential ways are there of arranging all the letters in the word MEDITERRANEN if all the vowels must be together and all the consonents must stay together, but the vowels and consonants can be arranged in any order. a c b d

2 Name: 8. How many five-member committees containing two Conservatives, two New Democrats, and one Liberal can be formed from seven Conservatives, six New Democrats, and five Liberals? a c b d ( n + 2)! 9. A simplified form of this expression would be n( n 1)! ( n + 2) ( n + 1) a. ( n + 2) ( n + 1) c. n ( n + 2) ( n + 1) ( n + 2) ( n + 1) b. d. ( n 1) ( n 1)! Numerical Response Use the following information to answer the next question The game of poker is played with a deck of 52 cards. The deck is broken up into four different suits of 13 cards each (clubs, diamonds, spades, and hearts) and each suit has 1 of the following cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. While there are variations of poker, this question deals with 5 Card Draw, where each player is given a starting hand with 5 cards. 10. Numerical Response: How many potential starting 5 card hands in poker could contain exactly two queens, exactly two aces and one other card. 11. Numerical Response: Determine the total number of paths leading from point A to point B if you must always be moving closer to point B B A 2

3 Name: 12. Numerical Response: If you were to expand the binomial expression, ( 3x 2) 6, what would be the value of the coefficient in front of the x 2 term? 13. Numerical Response: The sum of the following sequence; 12 C C C C 9 is 14. Numerical Response: How many ways are there of arranging two different mathematics books, three different history books, and four different French books side by side on a shelf if books of the same subject must be together? Use the following information to answer the next two questions The Funky Pickle Pizza Company is a very popular destination for people on Whyte Avenue in Edmonton as they have some of the best tasting pizza by the slice in the city. Suppose they have a selection of 20 toppings to choose from and that 1, 2 and 3 topping pizza slices all cost the same amount of money; four dollars. Pizza slices with more then 3 toppings cost more as they charge an additional 50 cents a topping for each additional topping. 15. Numerical Response: How many variations of a four topping pizza slice can be ordered from the Funky Pickle menu if one of the toppings has to be pepperoni? 16. Numerical Response: How many potential variations of pizza slices can be ordered where each individual slice costs four dollars? 3

4 Name: 17. Numerical Response: If you were to expand the binomial expression, 5x Ê ˆ, the Á x 2 th term would contain the constant term? 18. Numerical Response: The value of the fourteenth term in the 17th row of Pascal s triangle is. 19. Numerical Response: Determine the value for n in the folllowing equation: n P 3 = 5 Ê Á n 1 P Numerical Response: As part of their league schedule, the Athabasca hockey team must play each other team in their league three times in total. If there are a total of 8 other teams in this league, how many games are played in total all across the league? 21. Numerical Response: Suppose that four boys and three girls from Mr. MacDonald s latest drama production are arranging themselves in a line for a cast photo. How many ways can this photo potentially be taken if the star of the play, Vincent, must be in the center of the photo and both co-stars of the play, Kate and Mackenzie, must be adjacent to Vincent. 4

5 Permutations and Combinations Practice Test Answer Section MULTIPLE CHOICE 1. B 2. B 3. D 4. C 5. A 6. A 7. D 8. B 9. A SHORT ANSWER Ê Á C C C Ê 6! !4! 10! ˆ Á 6!4! Ê Á C C Ê Á C + C + C ( 16 C 13 ) ( 3) ( 2) 1 ( 1) ( 2)1 = 48 1

11.3B Warmup. 1. Expand: 2x. 2. Express the expansion of 2x. using combinations. 3. Simplify: a 2b a 2b

11.3B Warmup. 1. Expand: 2x. 2. Express the expansion of 2x. using combinations. 3. Simplify: a 2b a 2b 11.3 Warmup 1. Expand: 2x y 4 2. Express the expansion of 2x y 4 using combinations. 3 3 3. Simplify: a 2b a 2b 4. How many terms are there in the expansion of 2x y 15? 5. What would the 10 th term in